If in a finite strategic game all strategies are scalar, each player is only affected by the sum of the partners' choices, and one of three "single crossing" conditions is satisfied, then every best response improvement path leads to a Nash equilibrium. Journal of Economic Literature Classification Number: C 72. * Financial support from the Russian Foundation for Basic Research (grants 99-01-01238 and 02-01-00854), from the Russian state program for the support of the leading scientific schools (grant 00-15-96118), and from Generalitat Valenciana (grant INV 00-08-16) is acknowledged. I thank Francisco Marhuenda and Carmen Herrero for procuring the latter grant, and Universidad de Alicante, Departamento de Fundamentos del Análisis Económico, for its hospitality. Helpful comments by an anonymous referee and an associate editor are also appreciated.

No abstract

Nash equilibrium existence, Potential game, Congestion game, Additive aggregation,